📘 CONCEPT NOTES
📌 1. What is an Algebraic Identity?
An identity is an equation that is true for all values of variables.
👉 Example: (a + b)² = a² + 2ab + b²
📌 2. Important Algebraic Identities
🔹 Identity 1:
(a + b)² = a² + 2ab + b²
🔹 Identity 2:
(a − b)² = a² − 2ab + b²
🔹 Identity 3:
(a + b)(a − b) = a² − b²
🔹 Identity 4:
(x + a)(x + b) = x² + (a + b)x + ab
MCQs (50 Questions )
1. (a + b)² =
A) a² + b²
B) a² + 2ab + b²
C) a² − b²
D) 2a + 2b
Ans: B
2. (a − b)² =
A) a² − 2ab + b²
B) a² + 2ab + b²
C) a² − b²
D) a² + b²
Ans: A
3. (a + b)(a − b) =
A) a² + b²
B) a² − b²
C) 2ab
D) a² + 2ab
Ans: B
4. Identity means:
A) sometimes true
B) always true
C) never true
D) unknown
Ans: B
5. (x + 3)² =
A) x² + 9
B) x² + 6x + 9
C) x² − 6x + 9
D) x² + 3x
Ans: B
6. (2a)² =
A) 2a² B) 4a² C) a² D) 2a
Ans: B
7. (x + y)² expands to:
A) x² + y²
B) x² + 2xy + y²
C) x² − y²
D) xy
Ans: B
8. Identity is valid for:
A) specific values
B) no values
C) all values
D) negative values only
Ans: C
9. (a − b)(a + b) is called:
A) square identity
B) difference of squares
C) sum identity
D) product rule
Ans: B
10. (x − 5)² =
A) x² − 25
B) x² − 10x + 25
C) x² + 10x + 25
D) x² − 5x
Ans: B
📝 ASSERTION–REASON (10 Questions)
- A: Identities are true for all values
R: They are equations with variables
👉 A - A: (a − b)² = a² − b²
R: Identity ignores middle term
👉 C - A: (a + b)(a − b) = a² − b²
R: It is difference of squares
👉 A - A: Identity helps in quick calculation
R: It avoids multiplication
👉 B - A: (x + 1)² = x² + 1
R: Middle term is missing
👉 C
📊 NUMERICALS / EXPANSIONS
- (2x + 3)² = ?
👉 4x² + 12x + 9 - (x − 4)² = ?
👉 x² − 8x + 16 - (a + 5)(a − 5) = ?
👉 a² − 25 - (3x)² = ?
👉 9x² - (x + 2)(x + 3) = ?
👉 x² + 5x + 6
📄 FILL IN THE BLANKS
- (a + b)² = a² + ________ + b² → 2ab
- (a − b)² = a² − ________ + b² → 2ab
- (a + b)(a − b) = ________ → a² − b²
- Identity is true for ________ values → all
- Square of 2a is ________ → 4a²